Unfortunately for me, redownloading and reinstalling Safari 6 didn't fix my problem. Given that, say, twitter looks fine in Safari 6 on my MBP but not on my mini, I assume the problem is not with twitter but with something on my mini -- if not Safari, then something corrupted in ... I dunno, WebKit? Probably not Flash or Java, but I really wish Safari had the old Activity window so I could have more information.

Thanks, Steven. I had been trying various things like resetting Safari, clearing caches, etc., and it occurred to me a few hours ago that, since one of the problems I was having was unsuccessfully logging out of twitter, maybe I should force the issue by deleting the twitter-related cookies. Doing so resulted in my having to log back into twitter when I revisited the site, and now everything is fine. Somehow, my cookies got corrupted, which affected the appearance and functionality of the site.

As you suggested, logging in under a different OS X user account would have had the same result, since a fresh OS X user account would have had no old cookies.

(Oh, and while I was assuming Safari 6 had been corrupted, I went ahead and upgraded to Mountain Lion (which didn't fix the twitter problem, because, as noted, it seems to have been a cookie thing). Whole new-but-somehow-familiar can of worms, like restarting license managers when a license or two got lost or corrupted, reinstalling Java, reinstalling X11. It feels like just a month ago that I upgraded to Lion. This is probably a record for me of the shortest time residing in one OS (Lion).)